Rutile nano-TiO2 is a non-toxic and odorless inorganic UV shielding agent with excellent performance in polymer materials. This material absorbs part of the UV light energy through electronic transitions and releases it as heat or fluorescence. In this way, the molecular chain of the polymer material is prevented from being broken after absorbing high-energy ultraviolet light. So it has a certain antiaging effect. This article takes this material as the research object. We set up a molecular antiaging experiment for parametrically excited nonlinear differential equations. In this paper, the amplitude-frequency response of the system, the stability, and the bifurcation characteristics of the system are analyzed using the multiscale method. At the same time, we use numerical simulation to verify the theoretical analysis results. The research shows that the surface-treated nano-TiO2 has good dispersibility in polymer materials.